Which of the following plot is correct about the kinetic energy of photoelectrons ?

Options

A.
B.
C.
D.

Answer

To solve the question regarding the correct plot of the kinetic energy of photoelectrons, we will analyze the photoelectric effect and the relationships involved.

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
- When light of a suitable frequency strikes a metal surface, it causes the ejection of electrons from that surface. These ejected electrons are called photoelectrons.

2. **Energy Relation**:
- The energy of the incident light (E) can be expressed as:
\[ E = \text{Work Function} (\phi) + \text{Kinetic Energy}_{\text{max}} (KE_{\text{max}}) \]
- The work function (\(\phi\)) is the minimum energy required to eject an electron from the metal surface.

3. **Mathematical Representation**:
- The energy of the incident light can also be expressed as:
\[ E = h\nu \]
- Where \(h\) is Planck's constant and \(\nu\) is the frequency of the light. The work function can be expressed as:
\[ \phi = h\nu_0 \]
- Here, \(\nu_0\) is the threshold frequency.

4. **Kinetic Energy Expression**:
- Rearranging the energy equation gives:
\[ KE_{\text{max}} = h\nu - h\nu_0 \]
- This can also be expressed in terms of wavelength (\(\lambda\)):
\[ KE_{\text{max}} = \frac{hc}{\lambda} - h\nu_0 \]
- Where \(c\) is the speed of light.

5. **Relationship Between Kinetic Energy and Wavelength**:
- From the equation, we see that as the wavelength decreases (or frequency increases), the kinetic energy increases. This indicates an inverse relationship between kinetic energy and wavelength.

6. **Analyzing the Options**:
- **Option 1**: Kinetic energy vs. intensity - This plot is a horizontal line, indicating that kinetic energy does not change with intensity (only the number of photons increases).
- **Option 2**: Kinetic energy vs. frequency - This should show a direct relationship (not a constant).
- **Option 3**: Kinetic energy vs. wavelength - This should show an inverse relationship (not a constant).
- **Option 4**: Kinetic energy vs. surface area - This is not relevant to the photoelectric effect.

7. **Conclusion**:
- The correct plot that represents the relationship of kinetic energy of photoelectrons is **Option 1**, which shows that kinetic energy remains constant with increasing intensity.